报告题目 (title)：Analysis of Robin-boundary control for the Boussinesq equations
（Robin边界控制下Boussinesq方程的分析）
报告人 (Speaker)：龚伟 教授（中科院）
报告时间 (Time)：2025年12月16日（周二）10:00
报告地点 (Place)：#腾讯会议：216-802-379
邀请人(Inviter)：李新祥
主办部门：理学院数学系
报告摘要：In this talk, we study an optimal boundary control problem for the Boussinesq equations, which couple the time-dependent Navier-Stokes system with a heat equation, where the control enters through a Robin boundary condition on temperature. We begin by establishing the well-posedness of the optimization problem via a variational framework. We then derive both first- and second-order optimality conditions, including explicit characterizations of the adjoint state and the optimal control. Next, we perform a detailed numerical analysis of a fully discrete scheme: using finite elements in space and a semi-implicit scheme in time, combined with variational discretization for the control. We present rigorous a priori error estimates for the state, adjoint state, and control variables. Numerical experiments are provided to validate our theoretical results.
